Bargaining with Incomplete Information

A central question in economics is understanding the difficulties that parties have in reaching mutually beneficial agreements. Informational differences provide an appealing explanation for bargaining inefficiencies. This chapter provides an overview of the theoretical and empirical literature on bargaining with incomplete information. The chapter begins with an analysis of bargaining within a mechanism design framework. A modern development is provided of the classic result that, given two parties with independent private valuations, ex post efficiency is attainable if and only if it is common knowledge that gains from trade exist. The classic problems of efficient trade with one-sided incomplete information but interdependent valuations, and of efficiently dissolving a partnership with two-sided incomplete information, are also reviewed using mechanism design. The chapter then proceeds to study bargaining where the parties sequentially exchange offers. Under one-sided incomplete information, it considers sequential bargaining between a seller with a known valuation and a buyer with a private valuation. When there is a "gap" between the seller's valuation and the support of buyer valuations, the seller-offer game has essentially a unique sequential equilibrium. This equilibrium exhibits the following properties: it is stationary, trade occurs in finite time, and the price is favorable to the informed party (the Coase Conjecture). The alternating-offer game exhibits similar properties, when a refinement of sequential equilibrium is applied. However, in the case of "no gap" between the seller's valuation and the support of buyer valuations, the bargaining does not conclude with probability one after any finite number of periods, and it does not follow that sequential equilibria need be stationary. If stationarity is nevertheless assumed, then the results parallel those for the "gap" case. However, if stationarity is not assumed, then instead a folk theorem obtains, so substantial delay is possible and the uninformed party may receive substantial surplus. The chapter also briefly sketches results for sequential bargaining with two-sided incomplete information. Finally, it reviews the empirical evidence on strategic bargaining with private information by focusing on one of the most prominent examples of bargaining: union contract negotiations.Bargaining; Delay; Incomplete Information

A Generalized Theorem of the Maximum

This paper generalizes the Theorem of the Maximum (Berge, 1963) to allow for discontinuous changes in the domain and the objective function. It also provides a geometrical version of the (generalized) theorem.